In-class Exercise 5: Modeling the Spatial Variation of the Explanatory Factors of Water Points Status using Geographically Weighted Logistic Regression

Overview

In this in-class exercise, I learn how to use Geographically Weighted Logistic Regression to model the spatial variation of the explanatory factors of water points status.

Getting Started

In this exercise, the following R packages will be used:

  • sf for importing, managing, and processing geospatial data

  • spdep for computing spatial weights, global and local spatial autocorrelation statistics

  • tidyverse for importing, wrangling, and visualizing data

    • tidyr for manipulating data

    • dplyr for transforming data

    • ggplot2 for visualizing data

  • ggpubr for providing some easy-to-use functions for creating and customizing ggplot2

  • tmap for plotting cartographic quality choropleth map

  • corrplot for providing a visual exploratory tool on correlation matrix that supports automatic variable reordering to help detect hidden patterns among variables

  • GWmodel for calibrating geographical weighted family of models

  • funModeling for Exploratory Data Analysis (EDA)

  • blorr for building and validate binary logistic regression models

  • skimr for providing summary statistics about variables in data frames, tibbles, data tables and vectors

  • caret for training and plotting classification and regression models

The code chunk below installs and launch the R packages into R environment.

pacman::p_load(sf, spdep, tidyverse, ggpubr, tmap, corrplot,
               GWmodel, funModeling, blorr, skimr, caret)

Data Preparation

Importing data into R environment

The code chunk below uses read_rds() of Base R to import rds file Osun and Osun_wp_sf into R.

Osun <- read_rds("rds/Osun.rds")
Osun_wp_sf <- read_rds("rds/Osun_wp_sf.rds")

The code chunk below uses freq() of funModeling package to check the distribution of status field.

Osun_wp_sf %>%
  freq(input = 'status')
Warning: The `<scale>` argument of `guides()` cannot be `FALSE`. Use "none" instead as
of ggplot2 3.3.4.
ℹ The deprecated feature was likely used in the funModeling package.
  Please report the issue at <https://github.com/pablo14/funModeling/issues>.

  status frequency percentage cumulative_perc
1   TRUE      2642       55.5            55.5
2  FALSE      2118       44.5           100.0

Drawing statistical point map

The code chunk below uses tmap_mode() of tmap package to turn on the interactive mode.

tmap package is used to reveal the geospatial distribution of status.

set.zoom.limits argument of tm_view() sets the minimum and maximum zoom level to 9 and 12 respectively.

tmap_mode("view")
tmap mode set to interactive viewing
tm_shape(Osun) +
  tm_polygons(alpha = 0.4) +
 tm_shape(Osun_wp_sf) +
  tm_dots(col = 'status',
          alpha = 0.6) +
  tm_view(set.zoom.limits = c(9,12))

The code chunk below changes R display to plot mode.

tmap_mode("plot")
tmap mode set to plotting

The code chunk below uses skim() of skimr package to provide a broad overview of a data frame, which dispatches a set of summary functions based on the types of columns.

Osun_wp_sf %>%
  skim()
Warning: Couldn't find skimmers for class: sfc_POINT, sfc; No user-defined `sfl`
provided. Falling back to `character`.
Data summary
Name Piped data
Number of rows 4760
Number of columns 75
_______________________
Column type frequency:
character 47
logical 5
numeric 23
________________________
Group variables None

Variable type: character

skim_variable n_missing complete_rate min max empty n_unique whitespace
source 0 1.00 5 44 0 2 0
report_date 0 1.00 22 22 0 42 0
status_id 0 1.00 2 7 0 3 0
water_source_clean 0 1.00 8 22 0 3 0
water_source_category 0 1.00 4 6 0 2 0
water_tech_clean 24 0.99 9 23 0 3 0
water_tech_category 24 0.99 9 15 0 2 0
facility_type 0 1.00 8 8 0 1 0
clean_country_name 0 1.00 7 7 0 1 0
clean_adm1 0 1.00 3 5 0 5 0
clean_adm2 0 1.00 3 14 0 35 0
clean_adm3 4760 0.00 NA NA 0 0 0
clean_adm4 4760 0.00 NA NA 0 0 0
installer 4760 0.00 NA NA 0 0 0
management_clean 1573 0.67 5 37 0 7 0
status_clean 0 1.00 9 32 0 7 0
pay 0 1.00 2 39 0 7 0
fecal_coliform_presence 4760 0.00 NA NA 0 0 0
subjective_quality 0 1.00 18 20 0 4 0
activity_id 4757 0.00 36 36 0 3 0
scheme_id 4760 0.00 NA NA 0 0 0
wpdx_id 0 1.00 12 12 0 4760 0
notes 0 1.00 2 96 0 3502 0
orig_lnk 4757 0.00 84 84 0 1 0
photo_lnk 41 0.99 84 84 0 4719 0
country_id 0 1.00 2 2 0 1 0
data_lnk 0 1.00 79 96 0 2 0
water_point_history 0 1.00 142 834 0 4750 0
clean_country_id 0 1.00 3 3 0 1 0
country_name 0 1.00 7 7 0 1 0
water_source 0 1.00 8 30 0 4 0
water_tech 0 1.00 5 37 0 20 0
adm2 0 1.00 3 14 0 33 0
adm3 4760 0.00 NA NA 0 0 0
management 1573 0.67 5 47 0 7 0
adm1 0 1.00 4 5 0 4 0
New Georeferenced Column 0 1.00 16 35 0 4760 0
lat_lon_deg 0 1.00 13 32 0 4760 0
public_data_source 0 1.00 84 102 0 2 0
converted 0 1.00 53 53 0 1 0
created_timestamp 0 1.00 22 22 0 2 0
updated_timestamp 0 1.00 22 22 0 2 0
Geometry 0 1.00 33 37 0 4760 0
ADM2_EN 0 1.00 3 14 0 30 0
ADM2_PCODE 0 1.00 8 8 0 30 0
ADM1_EN 0 1.00 4 4 0 1 0
ADM1_PCODE 0 1.00 5 5 0 1 0

Variable type: logical

skim_variable n_missing complete_rate mean count
rehab_year 4760 0 NaN :
rehabilitator 4760 0 NaN :
is_urban 0 1 0.39 FAL: 2884, TRU: 1876
latest_record 0 1 1.00 TRU: 4760
status 0 1 0.56 TRU: 2642, FAL: 2118

Variable type: numeric

skim_variable n_missing complete_rate mean sd p0 p25 p50 p75 p100 hist
row_id 0 1.00 68550.48 10216.94 49601.00 66874.75 68244.50 69562.25 471319.00 ▇▁▁▁▁
lat_deg 0 1.00 7.68 0.22 7.06 7.51 7.71 7.88 8.06 ▁▂▇▇▇
lon_deg 0 1.00 4.54 0.21 4.08 4.36 4.56 4.71 5.06 ▃▆▇▇▂
install_year 1144 0.76 2008.63 6.04 1917.00 2006.00 2010.00 2013.00 2015.00 ▁▁▁▁▇
fecal_coliform_value 4760 0.00 NaN NA NA NA NA NA NA
distance_to_primary_road 0 1.00 5021.53 5648.34 0.01 719.36 2972.78 7314.73 26909.86 ▇▂▁▁▁
distance_to_secondary_road 0 1.00 3750.47 3938.63 0.15 460.90 2554.25 5791.94 19559.48 ▇▃▁▁▁
distance_to_tertiary_road 0 1.00 1259.28 1680.04 0.02 121.25 521.77 1834.42 10966.27 ▇▂▁▁▁
distance_to_city 0 1.00 16663.99 10960.82 53.05 7930.75 15030.41 24255.75 47934.34 ▇▇▆▃▁
distance_to_town 0 1.00 16726.59 12452.65 30.00 6876.92 12204.53 27739.46 44020.64 ▇▅▃▃▂
rehab_priority 2654 0.44 489.33 1658.81 0.00 7.00 91.50 376.25 29697.00 ▇▁▁▁▁
water_point_population 4 1.00 513.58 1458.92 0.00 14.00 119.00 433.25 29697.00 ▇▁▁▁▁
local_population_1km 4 1.00 2727.16 4189.46 0.00 176.00 1032.00 3717.00 36118.00 ▇▁▁▁▁
crucialness_score 798 0.83 0.26 0.28 0.00 0.07 0.15 0.35 1.00 ▇▃▁▁▁
pressure_score 798 0.83 1.46 4.16 0.00 0.12 0.41 1.24 93.69 ▇▁▁▁▁
usage_capacity 0 1.00 560.74 338.46 300.00 300.00 300.00 1000.00 1000.00 ▇▁▁▁▅
days_since_report 0 1.00 2692.69 41.92 1483.00 2688.00 2693.00 2700.00 4645.00 ▁▇▁▁▁
staleness_score 0 1.00 42.80 0.58 23.13 42.70 42.79 42.86 62.66 ▁▁▇▁▁
location_id 0 1.00 235865.49 6657.60 23741.00 230638.75 236199.50 240061.25 267454.00 ▁▁▁▁▇
cluster_size 0 1.00 1.05 0.25 1.00 1.00 1.00 1.00 4.00 ▇▁▁▁▁
lat_deg_original 4760 0.00 NaN NA NA NA NA NA NA
lon_deg_original 4760 0.00 NaN NA NA NA NA NA NA
count 0 1.00 1.00 0.00 1.00 1.00 1.00 1.00 1.00 ▁▁▇▁▁

Exploratory Data Analysis (EDA)

The code chunk below uses filter_at() to keep selected variables, remove NA values and all_vars() to change usage_capacity into numeric values.

Osun_wp_sf_clean <- Osun_wp_sf %>%
  filter_at(vars(status,
                 distance_to_primary_road,
                 distance_to_secondary_road,
                 distance_to_tertiary_road,
                 distance_to_city,
                 distance_to_town,
                 water_point_population,
                 local_population_1km,
                 usage_capacity,
                 is_urban,
                 water_source_clean),
            all_vars(!is.na(.))) %>%
  mutate(usage_capacity = as.factor(usage_capacity))

Correlation Analysis

The code chunk below selects the variables for analysis and saves into Osun_wp.

Osun_wp <- Osun_wp_sf_clean %>%
  select(c(7,35:39,42:43,46:47,57)) %>%
  st_set_geometry(NULL)

The code chunk below uses corrplot package to plot a scatterplot matrix of the relationship between the independent variables.

cluster_vars.cor = cor(
  Osun_wp[,2:7])
corrplot.mixed(cluster_vars.cor,
               lower = "ellipse",
               upper = "number",
               tl.pos = "lt",
               diag = "l",
               tl.col = "black")

Building a Logistic Regression Model

The code chunk below uses glm() to build a logistic regression model based on selected variables.

model <- glm(status ~
               distance_to_primary_road+
               distance_to_secondary_road+
               distance_to_city+
               distance_to_town+
               is_urban+
               usage_capacity+
               water_source_clean+
               water_point_population+
               local_population_1km,
             data = Osun_wp_sf_clean,
             family = binomial(link = 'logit'))

The code chunk below uses blr_regress() to show the result of model results.

blr_regress(model)
                             Model Overview                              
------------------------------------------------------------------------
Data Set    Resp Var    Obs.    Df. Model    Df. Residual    Convergence 
------------------------------------------------------------------------
  data       status     4756      4755           4745           TRUE     
------------------------------------------------------------------------

                    Response Summary                     
--------------------------------------------------------
Outcome        Frequency        Outcome        Frequency 
--------------------------------------------------------
   0             2114              1             2642    
--------------------------------------------------------

                                 Maximum Likelihood Estimates                                   
-----------------------------------------------------------------------------------------------
               Parameter                    DF    Estimate    Std. Error    z value     Pr(>|z|) 
-----------------------------------------------------------------------------------------------
              (Intercept)                   1      0.4828        0.1105      4.3699      0.0000 
        distance_to_primary_road            1      0.0000        0.0000     -1.5260      0.1270 
       distance_to_secondary_road           1      0.0000        0.0000     -0.8448      0.3982 
            distance_to_city                1      0.0000        0.0000     -3.6584       3e-04 
            distance_to_town                1      0.0000        0.0000     -4.1481      0.0000 
              is_urbanTRUE                  1     -0.3776        0.0799     -4.7261      0.0000 
           usage_capacity1000               1     -0.6547        0.0692     -9.4580      0.0000 
water_source_cleanProtected Shallow Well    1      0.4823        0.0854      5.6490      0.0000 
   water_source_cleanProtected Spring       1      1.2188        0.4380      2.7826      0.0054 
         water_point_population             1      -5e-04        0.0000    -11.1361      0.0000 
          local_population_1km              1      3e-04         0.0000     19.1424      0.0000 
-----------------------------------------------------------------------------------------------

 Association of Predicted Probabilities and Observed Responses  
---------------------------------------------------------------
% Concordant          0.7298          Somers' D        0.4597   
% Discordant          0.2702          Gamma            0.4597   
% Tied                0.0000          Tau-a            0.2270   
Pairs                5585188          c                0.7298   
---------------------------------------------------------------

The code chunk below uses blr_confusion_matrix() to create a confusion matrix of the above model.

blr_confusion_matrix(model, cutoff = 0.5)
Confusion Matrix and Statistics 

          Reference
Prediction FALSE TRUE
         0  1302  813
         1   812 1829

                Accuracy : 0.6583 
     No Information Rate : 0.4445 

                   Kappa : 0.3082 

McNemars's Test P-Value  : 1.0000 

             Sensitivity : 0.6923 
             Specificity : 0.6159 
          Pos Pred Value : 0.6925 
          Neg Pred Value : 0.6156 
              Prevalence : 0.5555 
          Detection Rate : 0.3846 
    Detection Prevalence : 0.5553 
       Balanced Accuracy : 0.6541 
               Precision : 0.6925 
                  Recall : 0.6923 

        'Positive' Class : 1

Building a Geographically Weighted Regression

Converting from sf to sp data frame

The code chunk below uses as_Spatial() to change Osun_wp_sf_clean data frame into spatial point object class.

Osun_wp_sp <- Osun_wp_sf_clean %>%
  select(c(status,
           distance_to_primary_road,
           distance_to_secondary_road,
           distance_to_tertiary_road,
           distance_to_city,
           distance_to_town,
           water_point_population,
           local_population_1km,
           usage_capacity,
           is_urban,
           water_source_clean)) %>%
  as_Spatial()
Osun_wp_sp
class       : SpatialPointsDataFrame 
features    : 4756 
extent      : 182502.4, 290751, 340054.1, 450905.3  (xmin, xmax, ymin, ymax)
crs         : +proj=tmerc +lat_0=4 +lon_0=8.5 +k=0.99975 +x_0=670553.98 +y_0=0 +a=6378249.145 +rf=293.465 +towgs84=-92,-93,122,0,0,0,0 +units=m +no_defs 
variables   : 11
names       : status, distance_to_primary_road, distance_to_secondary_road, distance_to_tertiary_road, distance_to_city, distance_to_town, water_point_population, local_population_1km, usage_capacity, is_urban, water_source_clean 
min values  :      0,        0.014461356813335,          0.152195902540837,         0.017815121653488, 53.0461399623541, 30.0019777713073,                      0,                    0,           1000,        0,           Borehole 
max values  :      1,         26909.8616132094,           19559.4793799085,          10966.2705628969,  47934.343603562, 44020.6393368124,                  29697,                36118,            300,        1,   Protected Spring 

Building fixed bandwidth GWR model

The code chunk below uses bw.ggwr() to build a fixed bandwidth GWR model based on selected variables.

bw.fixed <- bw.ggwr(status ~
                      distance_to_primary_road +
                      distance_to_secondary_road +
                      distance_to_tertiary_road +
                      distance_to_city +
                      distance_to_town +
                      water_point_population +
                      local_population_1km +
                      is_urban +
                      usage_capacity +
                      water_source_clean,
                    data = Osun_wp_sp,
                    family = "binomial",
                    approach = "AIC",
                    kernel = "gaussian",
                    adaptive = FALSE,
                    longlat = FALSE)
Take a cup of tea and have a break, it will take a few minutes.
          -----A kind suggestion from GWmodel development group
 Iteration    Log-Likelihood:(With bandwidth:  95768.67 )
=========================
       0        -2889 
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Fixed bandwidth: 95768.67 AICc value: 5684.357 
 Iteration    Log-Likelihood:(With bandwidth:  59200.13 )
=========================
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Fixed bandwidth: 59200.13 AICc value: 5646.785 
 Iteration    Log-Likelihood:(With bandwidth:  36599.53 )
=========================
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Fixed bandwidth: 36599.53 AICc value: 5575.148 
 Iteration    Log-Likelihood:(With bandwidth:  22631.59 )
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Fixed bandwidth: 22631.59 AICc value: 5466.883 
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Fixed bandwidth: 13998.93 AICc value: 5324.578 
 Iteration    Log-Likelihood:(With bandwidth:  8663.649 )
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Fixed bandwidth: 8663.649 AICc value: 5163.61 
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Fixed bandwidth: 5366.266 AICc value: 4990.587 
 Iteration    Log-Likelihood:(With bandwidth:  3328.371 )
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Fixed bandwidth: 3328.371 AICc value: 4798.288 
 Iteration    Log-Likelihood:(With bandwidth:  2068.882 )
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Fixed bandwidth: 2068.882 AICc value: 4837.017 
 Iteration    Log-Likelihood:(With bandwidth:  4106.777 )
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Fixed bandwidth: 4106.777 AICc value: 4873.161 
 Iteration    Log-Likelihood:(With bandwidth:  2847.289 )
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Fixed bandwidth: 2847.289 AICc value: 4768.192 
 Iteration    Log-Likelihood:(With bandwidth:  2549.964 )
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Fixed bandwidth: 2549.964 AICc value: 4762.212 
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Fixed bandwidth: 2366.207 AICc value: 4773.081 
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Fixed bandwidth: 2663.532 AICc value: 4762.568 
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Fixed bandwidth: 2479.775 AICc value: 4764.294 
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Fixed bandwidth: 2593.343 AICc value: 4761.813 
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Fixed bandwidth: 2620.153 AICc value: 4761.89 
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Fixed bandwidth: 2576.774 AICc value: 4761.889 
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Fixed bandwidth: 2603.584 AICc value: 4761.813 
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Fixed bandwidth: 2609.913 AICc value: 4761.831 
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Fixed bandwidth: 2599.672 AICc value: 4761.809 
 Iteration    Log-Likelihood:(With bandwidth:  2597.255 )
=========================
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Fixed bandwidth: 2597.255 AICc value: 4761.809 

The code chunk below shows the optimal fixed bandwidth.

bw.fixed
[1] 2599.672
gwlr.fixed <- ggwr.basic(status ~
                      distance_to_primary_road +
                      distance_to_secondary_road +
                      distance_to_tertiary_road +
                      distance_to_city +
                      distance_to_town +
                      water_point_population +
                      local_population_1km +
                      is_urban +
                      usage_capacity +
                      water_source_clean,
                    data = Osun_wp_sp,
                    bw = 2599.672,
                    family = "binomial",
                    kernel = "gaussian",
                    adaptive = FALSE,
                    longlat = FALSE)
 Iteration    Log-Likelihood
=========================
       0        -1958 
       1        -1676 
       2        -1526 
       3        -1443 
       4        -1405 
       5        -1405 

The code chunk below shows the model results and the AIC value indicates that the model improves.

gwlr.fixed
   ***********************************************************************
   *                       Package   GWmodel                             *
   ***********************************************************************
   Program starts at: 2022-12-17 17:47:11 
   Call:
   ggwr.basic(formula = status ~ distance_to_primary_road + distance_to_secondary_road + 
    distance_to_tertiary_road + distance_to_city + distance_to_town + 
    water_point_population + local_population_1km + is_urban + 
    usage_capacity + water_source_clean, data = Osun_wp_sp, bw = 2599.672, 
    family = "binomial", kernel = "gaussian", adaptive = FALSE, 
    longlat = FALSE)

   Dependent (y) variable:  status
   Independent variables:  distance_to_primary_road distance_to_secondary_road distance_to_tertiary_road distance_to_city distance_to_town water_point_population local_population_1km is_urban usage_capacity water_source_clean
   Number of data points: 4756
   Used family: binomial
   ***********************************************************************
   *              Results of Generalized linear Regression               *
   ***********************************************************************

Call:
NULL

Deviance Residuals: 
     Min        1Q    Median        3Q       Max  
-124.555    -1.755     1.072     1.742    34.333  

Coefficients:
                                           Estimate Std. Error z value Pr(>|z|)
Intercept                                 3.887e-01  1.124e-01   3.459 0.000543
distance_to_primary_road                 -4.642e-06  6.490e-06  -0.715 0.474422
distance_to_secondary_road               -5.143e-06  9.299e-06  -0.553 0.580230
distance_to_tertiary_road                 9.683e-05  2.073e-05   4.671 3.00e-06
distance_to_city                         -1.686e-05  3.544e-06  -4.757 1.96e-06
distance_to_town                         -1.480e-05  3.009e-06  -4.917 8.79e-07
water_point_population                   -5.097e-04  4.484e-05 -11.369  < 2e-16
local_population_1km                      3.451e-04  1.788e-05  19.295  < 2e-16
is_urbanTRUE                             -2.971e-01  8.185e-02  -3.629 0.000284
usage_capacity1000                       -6.230e-01  6.972e-02  -8.937  < 2e-16
water_source_cleanProtected Shallow Well  5.040e-01  8.574e-02   5.878 4.14e-09
water_source_cleanProtected Spring        1.288e+00  4.388e-01   2.936 0.003325
                                            
Intercept                                ***
distance_to_primary_road                    
distance_to_secondary_road                  
distance_to_tertiary_road                ***
distance_to_city                         ***
distance_to_town                         ***
water_point_population                   ***
local_population_1km                     ***
is_urbanTRUE                             ***
usage_capacity1000                       ***
water_source_cleanProtected Shallow Well ***
water_source_cleanProtected Spring       ** 
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 6534.5  on 4755  degrees of freedom
Residual deviance: 5688.0  on 4744  degrees of freedom
AIC: 5712

Number of Fisher Scoring iterations: 5


 AICc:  5712.099
 Pseudo R-square value:  0.1295351
   ***********************************************************************
   *          Results of Geographically Weighted Regression              *
   ***********************************************************************

   *********************Model calibration information*********************
   Kernel function: gaussian 
   Fixed bandwidth: 2599.672 
   Regression points: the same locations as observations are used.
   Distance metric: A distance matrix is specified for this model calibration.

   ************Summary of Generalized GWR coefficient estimates:**********
                                                   Min.     1st Qu.      Median
   Intercept                                -8.7229e+02 -4.9955e+00  1.7600e+00
   distance_to_primary_road                 -1.9389e-02 -4.8031e-04  2.9618e-05
   distance_to_secondary_road               -1.5921e-02 -3.7551e-04  1.2317e-04
   distance_to_tertiary_road                -1.5618e-02 -4.2368e-04  7.6179e-05
   distance_to_city                         -1.8416e-02 -5.6217e-04 -1.2726e-04
   distance_to_town                         -2.2411e-02 -5.7283e-04 -1.5155e-04
   water_point_population                   -5.2208e-02 -2.2767e-03 -9.8875e-04
   local_population_1km                     -1.2698e-01  4.9952e-04  1.0638e-03
   is_urbanTRUE                             -1.9790e+02 -4.2908e+00 -1.6864e+00
   usage_capacity1000                       -2.0772e+01 -9.7231e-01 -4.1592e-01
   water_source_cleanProtected.Shallow.Well -2.0789e+01 -4.5190e-01  5.3340e-01
   water_source_cleanProtected.Spring       -5.2235e+02 -5.5977e+00  2.5441e+00
                                                3rd Qu.      Max.
   Intercept                                 1.2763e+01 1073.2156
   distance_to_primary_road                  4.8443e-04    0.0142
   distance_to_secondary_road                6.0692e-04    0.0258
   distance_to_tertiary_road                 6.6815e-04    0.0128
   distance_to_city                          2.3718e-04    0.0150
   distance_to_town                          1.9271e-04    0.0224
   water_point_population                    5.0102e-04    0.1309
   local_population_1km                      1.8157e-03    0.0392
   is_urbanTRUE                              1.2841e+00  744.3099
   usage_capacity1000                        3.0322e-01    5.9281
   water_source_cleanProtected.Shallow.Well  1.7849e+00   67.6343
   water_source_cleanProtected.Spring        6.7663e+00  317.4133
   ************************Diagnostic information*************************
   Number of data points: 4756 
   GW Deviance: 2795.084 
   AIC : 4414.606 
   AICc : 4747.423 
   Pseudo R-square value:  0.5722559 

   ***********************************************************************
   Program stops at: 2022-12-17 17:48:09 

Model Assessment

Converting SDF into sf data frame

To assess the performance of the gwlr, we suse the code chunk below convert SDF object into data frame.

gwr.fixed <- as.data.frame(gwlr.fixed$SDF)

The code chunk below label yhat values >= 0.5 into 1 and else 0. The result is saved into a field called most.

gwr.fixed <- gwr.fixed %>%
  mutate(most = ifelse(
    gwr.fixed$yhat >= 0.5, T, F))
gwr.fixed$y <- as.factor(gwr.fixed$y)
gwr.fixed$most <- as.factor(gwr.fixed$most)
CM <- confusionMatrix(data = gwr.fixed$most,
                      reference = gwr.fixed$y)
CM
Confusion Matrix and Statistics

          Reference
Prediction FALSE TRUE
     FALSE  1824  263
     TRUE    290 2379
                                          
               Accuracy : 0.8837          
                 95% CI : (0.8743, 0.8927)
    No Information Rate : 0.5555          
    P-Value [Acc > NIR] : <2e-16          
                                          
                  Kappa : 0.7642          
                                          
 Mcnemar's Test P-Value : 0.2689          
                                          
            Sensitivity : 0.8628          
            Specificity : 0.9005          
         Pos Pred Value : 0.8740          
         Neg Pred Value : 0.8913          
             Prevalence : 0.4445          
         Detection Rate : 0.3835          
   Detection Prevalence : 0.4388          
      Balanced Accuracy : 0.8816          
                                          
       'Positive' Class : FALSE           
                                          

Visualizing gwLR

Osun_wp_sf_selected <- Osun_wp_sf_clean %>%
  select(c(ADM2_EN, ADM2_PCODE, ADM1_EN, ADM1_PCODE, status))
gwr_sf.fixed <- cbind(Osun_wp_sf_selected, gwr.fixed)

Visualizing coefficient estimates

tmap_mode("view")
tmap mode set to interactive viewing
prob_T <- tm_shape(Osun) +
  tm_polygons(alpha = 0.1) +
tm_shape(gwr_sf.fixed) +
  tm_dots(col = "yhat",
          border.col = "gray60",
          border.lwd = 1) +
  tm_view(set.zoom.limits = c(8,14))
prob_T
tertiary_TV <- tm_shape(Osun) +
  tm_polygons(alpha = 0.1) +
tm_shape(gwr_sf.fixed) +
  tm_dots(col = "distance_to_tertiary_road_TV",
          border.col = "gray60",
          border.lwd = 1) +
  tm_view(set.zoom.limits = c(8,14))
tertiary_TV
Variable(s) "distance_to_tertiary_road_TV" contains positive and negative values, so midpoint is set to 0. Set midpoint = NA to show the full spectrum of the color palette.
tmap_mode("plot")
tmap mode set to plotting

Removing insignificant variables

According to the generalized linear regression model and geographically weighted regression model results, distance_to_primary_road and distance_to_secondary_road are not significant. Therefore, these 2 variables are removed and conduct analysis again.

bw.fixed2 <- bw.ggwr(status ~
                      distance_to_tertiary_road +
                      distance_to_city +
                      distance_to_town +
                      water_point_population +
                      local_population_1km +
                      is_urban +
                      usage_capacity +
                      water_source_clean,
                    data = Osun_wp_sp,
                    family = "binomial",
                    approach = "AIC",
                    kernel = "gaussian",
                    adaptive = FALSE,
                    longlat = FALSE)
Take a cup of tea and have a break, it will take a few minutes.
          -----A kind suggestion from GWmodel development group
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bw.fixed2
[1] 2377.371
gwlr.fixed2 <- ggwr.basic(status ~
                      distance_to_tertiary_road +
                      distance_to_city +
                      distance_to_town +
                      water_point_population +
                      local_population_1km +
                      is_urban +
                      usage_capacity +
                      water_source_clean,
                    data = Osun_wp_sp,
                    bw = 2377.371,
                    family = "binomial",
                    kernel = "gaussian",
                    adaptive = FALSE,
                    longlat = FALSE)
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gwlr.fixed2
   ***********************************************************************
   *                       Package   GWmodel                             *
   ***********************************************************************
   Program starts at: 2022-12-17 18:04:02 
   Call:
   ggwr.basic(formula = status ~ distance_to_tertiary_road + distance_to_city + 
    distance_to_town + water_point_population + local_population_1km + 
    is_urban + usage_capacity + water_source_clean, data = Osun_wp_sp, 
    bw = 2377.371, family = "binomial", kernel = "gaussian", 
    adaptive = FALSE, longlat = FALSE)

   Dependent (y) variable:  status
   Independent variables:  distance_to_tertiary_road distance_to_city distance_to_town water_point_population local_population_1km is_urban usage_capacity water_source_clean
   Number of data points: 4756
   Used family: binomial
   ***********************************************************************
   *              Results of Generalized linear Regression               *
   ***********************************************************************

Call:
NULL

Deviance Residuals: 
     Min        1Q    Median        3Q       Max  
-129.368    -1.750     1.074     1.742    34.126  

Coefficients:
                                           Estimate Std. Error z value Pr(>|z|)
Intercept                                 3.540e-01  1.055e-01   3.354 0.000796
distance_to_tertiary_road                 1.001e-04  2.040e-05   4.910 9.13e-07
distance_to_city                         -1.764e-05  3.391e-06  -5.202 1.97e-07
distance_to_town                         -1.544e-05  2.825e-06  -5.466 4.60e-08
water_point_population                   -5.098e-04  4.476e-05 -11.390  < 2e-16
local_population_1km                      3.452e-04  1.779e-05  19.407  < 2e-16
is_urbanTRUE                             -2.667e-01  7.474e-02  -3.569 0.000358
usage_capacity1000                       -6.206e-01  6.966e-02  -8.908  < 2e-16
water_source_cleanProtected Shallow Well  4.947e-01  8.496e-02   5.823 5.79e-09
water_source_cleanProtected Spring        1.279e+00  4.384e-01   2.917 0.003530
                                            
Intercept                                ***
distance_to_tertiary_road                ***
distance_to_city                         ***
distance_to_town                         ***
water_point_population                   ***
local_population_1km                     ***
is_urbanTRUE                             ***
usage_capacity1000                       ***
water_source_cleanProtected Shallow Well ***
water_source_cleanProtected Spring       ** 
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 6534.5  on 4755  degrees of freedom
Residual deviance: 5688.9  on 4746  degrees of freedom
AIC: 5708.9

Number of Fisher Scoring iterations: 5


 AICc:  5708.923
 Pseudo R-square value:  0.129406
   ***********************************************************************
   *          Results of Geographically Weighted Regression              *
   ***********************************************************************

   *********************Model calibration information*********************
   Kernel function: gaussian 
   Fixed bandwidth: 2377.371 
   Regression points: the same locations as observations are used.
   Distance metric: A distance matrix is specified for this model calibration.

   ************Summary of Generalized GWR coefficient estimates:**********
                                                   Min.     1st Qu.      Median
   Intercept                                -3.7021e+02 -4.3797e+00  3.5590e+00
   distance_to_tertiary_road                -3.1622e-02 -4.5462e-04  9.1291e-05
   distance_to_city                         -5.4555e-02 -6.5623e-04 -1.3507e-04
   distance_to_town                         -8.6549e-03 -5.2754e-04 -1.6785e-04
   water_point_population                   -2.9696e-02 -2.2705e-03 -1.2277e-03
   local_population_1km                     -7.7730e-02  4.4281e-04  1.0548e-03
   is_urbanTRUE                             -7.3554e+02 -3.4675e+00 -1.6596e+00
   usage_capacity1000                       -5.5889e+01 -1.0347e+00 -4.1960e-01
   water_source_cleanProtected.Shallow.Well -1.8842e+02 -4.7295e-01  6.2378e-01
   water_source_cleanProtected.Spring       -1.3630e+03 -5.3436e+00  2.7714e+00
                                                3rd Qu.      Max.
   Intercept                                 1.3755e+01 2171.6375
   distance_to_tertiary_road                 6.3011e-04    0.0237
   distance_to_city                          1.5921e-04    0.0162
   distance_to_town                          2.4490e-04    0.0179
   water_point_population                    4.5879e-04    0.0765
   local_population_1km                      1.8479e-03    0.0333
   is_urbanTRUE                              1.0554e+00  995.1841
   usage_capacity1000                        3.9113e-01    9.2449
   water_source_cleanProtected.Shallow.Well  1.9564e+00   66.8914
   water_source_cleanProtected.Spring        7.0805e+00  208.3749
   ************************Diagnostic information*************************
   Number of data points: 4756 
   GW Deviance: 2815.659 
   AIC : 4418.776 
   AICc : 4744.213 
   Pseudo R-square value:  0.5691072 

   ***********************************************************************
   Program stops at: 2022-12-17 18:04:53